Quadrilateral Formed by Centre, Any Two Points on the Circle and Point of Intersection of Tangents

Q.

In the given figure , AC and BC are tangents to the circle with centre O.

If $\angle ACB$ is twice $\angle AOB$ , then $\angle ACB$ = ____

1. ${150}^{\circ }$

2. ${120}^{\circ }$

3. ${100}^{\circ }$

4. ${60}^{\circ }$

Q.

If the sides of a parallelogram touch a circle, then the parallelogram is a rhombus.

1. True
2. False

Q.

Circles with centres P and Q intersect at points A and B as shown in the figure. CBD is a line segment and EBM is tangent to the circle, with centre Q, at point B. If the circles are congruent; Then, CE = ________

1. BD

2. 3BD

3. 7BD

4. 2BD

Q. Prove that there is ona and only one tangent at any point on the circumference of a circle.

Q. Two tangents can be drawn to a circle from a point outside the circle.

1. True
2. False

Q.

In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If $\angle BAC={30}^{\circ }$, then $\angle ACD=$ ______.

1. ${120}^{\circ }$

2. ${100}^{\circ }$

3. ${30}^{\circ }$

4. ${60}^{\circ }$

Q.
$\text{If TP and TQ are two tangents to a circle}\text{with center O such that}\angle POQ={110}^o,\text{then}\angle PTQ\text{will be}$.

1. ${70}^{\circ }$
2. ${80}^{\circ }$
3. ${90}^{\circ }$

Q. Two tangents can be drawn to a circle from a point outside the circle.

1. True
2. False

Q.

In the given figure , AC and BC are tangents to the circle with centre O.

If $\angle ACB$ is twice $\angle AOB$ , then find the $\angle ACB$.

Q.

In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If $\angle BAC={30}^{\circ }$, then $\angle CDB=$ ______.

1. ${120}^{\circ }$

2. ${30}^{\circ }$

3. ${100}^{\circ }$

4. ${60}^{\circ }$

Q. How many tangents can be drawn from a point inside the circle?

1. 4
2. 0
3. 1
4. 2

Q.

In figure displayed below, if TP and TQ are the two tangents to a circle with centre O so that $\angle POQ={110}^{\circ },then\angle PTQ$ is equal to

1. ${70}^{\circ }$

2. ${50}^{\circ }$

3. ${90}^{\circ }$

4. ${80}^{\circ }$

Q. In the given figure, O is the centre of the circle. PQ is the tangent to the circle at A. If $\angle$ PAB = 60${}^0$ then find $\angle$ABO.

1. 30${}^0$
2. 60${}^0$
3. 90${}^0$
4. Can't be found

Q. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of ${80}^{\circ },$ then $\angle POA$ is equal to

Q. In the given figure, PQ and PR are two tangents drawn from an external point P to a circle with centre 'O'. If OQ = 3 cm and PS = 2 cm then, find the perimeter (in cm) of quadrilateral PQOR.

1. 14

Q. $\text{In the given figure, ABCD is a}\text{quadrilateral circumscribing a circle with}\text{centre 'O'. If}\angle B={90}^{\circ },AD=23cm,AB=29cm\text{and}DS=5cm,\text{then find}\text{the radius of the circle.}$

1. 11 cm
2. 12 cm
3. 14 cm
4. 9 cm

Q. In the given figure, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 56°, then calculate ∠QOR. [1 mark]

Q. If from a point P two tangents can be drawn to a circle, then P is the circle.

1. outside
2. inside
3. on

Q. In the given figure, O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If $\angle$ TPQ = ${70}^o$, find $\angle$ TRQ.

Q. In the given figure, if TP and TQ are the two tangents to a circle with centre O so that $\angle POQ={110}^{\circ },\angle PTQ$ is equal to

Q. How many tangents can be drawn to a circle from a point outside the circle?

1. 0
2. 1
3. 2
4. 3

Q. PQ and PR are two tangents drawn from a point P. If centre 'O' of the circle and P are joined, then
$\angle OPR:\angle OPQ$ =.

1. $2:1$
2. $1:1$
3. $1:2$
4. $4:1$

Q. In the given figure, if TP and TQ are the two tangents to a circle with centre O so that $\angle POQ={110}^{\circ },\angle PTQ$ is equal to

Q. Draw a circle of any radius. From a point outside the circle, draw tangents to the circle inclined at 45${}^{\circ }$ to each other.

Q. In the given figure, O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If $\angle$ TPQ = ${70}^o$, find $\angle$ TRQ.

Q. In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If $\angle BAC={30}^{\circ }$, then find the value of $\angle CDB$ [3 Marks]

Q. In the given figure, R is an external point and RP and RQ are tangents drawn to the circle from R. $\angle POQis{90}^{\circ }$. Prove that OPRQ is a prarallelogram, and find the $\angle$ POR.

Q. In figure, $AP,AQ$ and $BC$ are tangents of the circle with centre $O$. If $AB=5cm,AC=6cm$ and $BC=4$ $cm$, then the length of $AP($ in $cm)$ is

1. 9
2. 15
3. 10
4. 7.5

Q. In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If $\angle BAC={30}^{\circ }$, then find $\angle CDB$.

Q.

In the given figure , AC and BC are tangents to the circle with centre O.

If $\angle ACB$ is twice $\angle AOB$ , then find the $\angle ACB$.